化學反應工程英文課件Chapter 5

化學反應工程Chapter5

IdealReactorsforaSingleReaction

InthischapterwedeveloptheperformanceequationforasinglefluidreactinginthethreeidealreactorsshowninFig.5.1.Wecallthesehomogeneousreactions.Inthebatchreactor,orBR,ofFig.5.1athereactantsareinitiallychargedintoacontainer,arewellmixed,andarelefttoreactforacertainperiod.Theresultantmixtureisthendischarged.Thisisanunsteady-stateoperationwherecompositionchangeswithtime;however,atanyinstantthecompositionthroughoutthereactorisuniform.化學反應工程BatchReactorMixedFlowReactor化學反應工程Thefirstofthetwoidealsteady-stateflowreactorsisvariouslyknownastheplugflow,slugflow,pistonflow,idealtubular,andunmixedflowreactor,anditisshowninFig.5.1b.Werefertoitastheplugflowreactor,orPFR,andtothispatternofflowasplugflow.Itischaracterizedbythefactthattheflowoffluidthroughthereactorisorderlywithnoelementoffluidovertakingormixingwithanyotherelementaheadorbehind.Actually,theremaybelateralmixingoffluidinaplugflowreactor;however,theremustbenomixingordiffusionalongtheflowpath.Thenecessaryandsufficientconditionforplugflowisfortheresidencetimeinthereactortobethesameforallelementoffluid.化學反應工程Theotheridealsteady-stateflowreactoriscalledthemixedreactor,thebackmixreactor,theidealstirredtankreactor,theC*(meaningC-star),CSTR,ortheCFSTR(constantflowstirredtankreactor)and,asitsnamessuggest,itisareactorinwhichthecontentsarewellstirredanduniformthroughout.Thus,theexitstreamfromthisreactorhasthesamecompositionasthefluidwithinthereactor.Werefertothistypeofflowas

mixedflow,andthecorrespondingreactorthemixedflowreactor,orMFR.Thesethreeidealsarerelativelyeasytotreat.Inaddition,oneorotherusuallyrepresentsthebestwayofcontactingthereactants－nomatterwhattheoperation.Thesteadyandunsteadyoperation間歇操作(Batchreactor,BR)連續(xù)操作(MixedFlowReactor,MFR)

連續(xù)操作(PlugFlowReactor,PFR)化學反應工程Forthesereasons,weoftentrytodesignrealreactorssothattheirflowsapproachtheseideals,andmuchofthedevelopmentinthisbookcentersaboutthem.InthetreatmenttofollowitshouldbeunderstoodthatthetermV,calledthereactorvolume,reallyreferstothevolumeoffluidinthereactor.Whenthisdiffersfromtheinternalvolumeofreactor,thenVr

‘designates(指明,任命)theinternalvolumeofreactorwhileV

designatesthevolumeofreactingfluid.Forexample,insolidcatalyzedreactorswithvoidage(空隙率)

wehaveV=

VrForhomogeneoussystems,however,weusuallyusethetermValone.化學反應工程5.1IDEALBATCHREACTOR

MakeamaterialbalanceforanycomponentA.Forsuchaaccountingweusuallyselectthelimitingcomponent.Inabatchreactor,sincethecompositionisuniformthroughoutatanyinstantoftime,wemaymaketheaccountingaboutthewholereactor.Notingthatnofluidentersorleavesthereactionmixtureduringreaction,Eq.4.1,whichwaswrittenforcomponentA,becomes

input=output+disappearance+accumulation

or化學反應工程EvaluatingthetermsofEq.1,wefind化學反應工程ByreplacingthesetwotermsinEq.1,weobtain

(2)

Rearrangingandintegratingthengives(3)

ThisisthegeneralequationshowingthetimerequiredtoachieveaconversionXAforeitherisothermalornonisothermaloperation.Thevolumeofreactingfluidandthereactionrate

remainundertheintegralsign,foringeneraltheybothchangeasreactionproceed.化學反應工程Thisequationmaybesimplifiedforanumberofsituations.Ifthedensityofthefluidremainsconstant,weobtain

(4)

Forallreactionsinwhichthevolumeofreactingmixturechangesproportionatelywithconversion,suchasinsinglegas-phasereactionswithsignificantdensitychanges,Eq.3becomes

(5)

化學反應工程Inoneformoranother,Eqs.2to5haveallbeenencounteredinChapter3.Theyareapplicabletobothisothermalandnonisothermaloperations.Forthelatterthevariationofratewithtemperature,andthevariationoftemperaturewithconversion,mustbeknownbeforesolutionispossible.Figure5.2isagraphicalrepresentationoftwooftheseequations.化學反應工程化學反應工程Space-TimeandSpace-VelocityJustasthereactiontimetisthenatureperformancemeasureforabatchreactor,soarethespace-timeandspace-velocitytheproperperformancemeasureofflowreactors.Thesetermsaredefinedasfollows:

Space-time:

(6)

化學反應工程Space-velocity:

(7)

Thus,aspace-velocityof5hr-1meansthatfivereactorvolumesoffeedatspecifiedconditionsarebeingfedintothereactorperhour.Aspace-timeof2minmeansthatevery2minonereactorvolumeoffeedatspecifiedconditionsisbeingtreatedbythereactor.化學反應工程Nowwemayarbitrarilyselectthetemperature,pressure,andstate(gas,liquid,orsolid)atwhichwechoosetomeasurethevolumeofmaterialbeingfedtothereactor.Certainly,then,thevalueforspace-velocityorspace-timedependsontheconditionsselected.Iftheyareofthestreamenteringthereactor,therelationbetweensandandtheotherpertinent(有關的)variableis(8)

化學反應工程Itmaybemoreconvenienttomeasurethevolumetricfeedrateatsomestandardstate,especiallywhenthereactoristooperateatanumberoftemperatures.If,forexample,thematerialisgaseouswhenfedtothereactorathightemperaturebutisliquidatthestandardstate,caremustbetakentospecify(指定)pre’ciselywhatstatehasbeenchosen.Therelationbetweenthespace-velocityandspace-timeforactualfeedconditions(unprimed不加撇號的symbols)andatstandardconditions(designatedbyprimes)isgivenby(9)

化學反應工程5.2STEADY-STATEMIXEDFLOWREACTION

TheperformanceequationforthemixedflowreactorisobtainedfromEq.4.1,whichmakesanaccountingforagivencomponentwithinanelementofvolumeofthesystem.Butsincethecompositionisuniformthroughout,theaccountingmaybemadeaboutthereactorasawhole.ByselectingreactantAforconsideration,Eq.4.1becomes

Input=output+disappearancebyreaction+accumulation

(10)

=0化學反應工程Figure5.3

Notation(符號)foramixedreactor.

化學反應工程AsshowninFig.5.3.IfisthemolarfeedrateofcomponentAtothereactor,thenconsideringthereactorasawholewehave

inputofA,moles/time=FA0(1-XA0)=FA0outputofA,moles/time=FA=FA0(1-XA)

=IntroducingthesethreetermsintoEq.10,weobtain

化學反應工程whichonrearrangementbecomes

orany(11)

WhereXA0=0,soXA=XA-XA0=

XA.XA

andrA

aremeasuredatexitstreamconditions,whicharethesameastheconditionswithinthereactor.化學反應工程Moregenerally,ifthefeedonwhichconversionisbased,subscript0,entersthereactorpartiallyconverted,subscripti,andleavesatconditionsgivenbysubscriptf,wehave

or(12)

whereXA,i0化學反應工程Forthespecialcaseofconstant-densitysystems

XA=1-CA/CA0,inwhichcasetheperformanceequationformixedreactorscanalsobewrittenintermsofconcentrationsoror(13)

TheseexpressionsrelateinasimplewaythefourtermsXA,rA

,V,FA0;thus,knowinganythreeallowsthefourthtobefounddirectly.Figure5.4isagraphicalrepresentationofthesemixedflowperformanceequations.化學反應工程Figure5.4

Graphicalrepresentationofthedesignequationsformixedflowreactor.0XAXAGeneralcaseArea=FromEq.11Constant-densitysystemsonlyCA0CA0CAArea=FromEq.13Conditionswithinreactorandatexit化學反應工程EXAMPLE5.1REACTIONRATEINAMIXEDFLOWREACTOR

OneliterperminuteofliquidcontainingAandB(CA0=0.10mol/liter,CB0

=0.01mol/liter)flowintoamixedreactorofvolumeV=1liter.Thematerialsreactinacomplexmannerforwhichthestoichiometryisunknown.TheoutletstreamfromthereactorcontainsA,BandC(CAf=0.02mol/liter,CBf=0.03mol/liter,CCf=0.04mol/literasshowninFig.E5.1.FindtherateofreactionofA,BandCfortheconditionswithinthereactor.化學反應工程FigureE5.1

化學反應工程SOLUTION

ForaliquidinamixedflowreactorA=0andEq.13appliestoeachofthereactingcomponents,givingfortherateofdisappearance:ThusAisdisappearingwhileBandCarebeingformed.

化學反應工程EXAMPLE5.2KINETICSFROMAMIXEDFLOWREACTOR

PuregaseousreactantA(CA0=100millimol/liter)isfedatasteadyrateintoamixedflowreactor(V=0.1liter)whereitdimerizes(2AR).Fordifferentgasfeedratesthefollowingdataareobtained:Runnumber123410.03.01.20.5millimol/liter85.766.75033.4

Findarateequationforthisreaction.化學反應工程SOLUTION

Forthisstoichiometry,2AR,theexpansionfactoris

andthecorrespondingrelationbetweenconcentrationandconversionisor化學反應工程Theconversionforeachrunisthencalculatedandtabulatedincolumn4ofTableE5.2.TableE5.2logCAlog(-rA)

23.066.70.5015001.8243.17631.2500.6678001.6992.93040.533.30.804001.5222.602

Calculated化學反應工程Fromtheperformanceequation,Eq.11,therateofreactionforeachrunisgivenbyThesevaluesaretabulatedincolumn5ofTableE5.2.

HavingpairedvaluesofrAandCA

(seeTableE5.2)wearereadytotestvariouskineticexpressions.Insteadofseparatelytestingforfirst-order(plotrA

vs.CA

),second-order(plotrA

vs.),etc.,letustestdirectlyfornth-orderkinetics.Forthistakelogarithmsof,giving

化學反應工程021234log（-rA）Slope=3.398-2.6021.933-1.522Fitthelowestpoint400=k(33.3)2∴k=0.36logCAFigureE5.2=1.93≈2化學反應工程Comment.Ifweignorethedensitychangeinouranalysis(orput=0anduseweendupwithanincorrectrateequation(reactionordern

1.6

)whichwhenusedindesignwouldgivewrongperformanceprediction.

Fornth-orderkineticsthisdatashouldgiveastraightlineonalog(-rA)vs.logCAplot.Fromcolumns6and7ofTableE5.2andasshowninFig.E5.2,thefourdatapointsarereasonablyrepresentedbyastraightlineofslope2,sotherateequationforthisdimerizationis化學反應工程EXAMPLE5.3MIXEDFLOWREACTORPERFORMANCE

Theelementaryliquid-phasereactionA+2BRwithrateequationistotakeplaceina6-litersteady-statemixedflowreactor.Twofeedstreams,onecontaining2.8molA/literandtheothercontaining1.6molB/liter,aretobeintroducedatequalvolumetricflowratesintothereactor,and75%conversionoflimitingcomponentisdesired(seeFig.E5.3).Whatshouldbetheflowrateofeachstream?Assumeaconstantdensitythroughout.

化學反應工程FigureE5.3

化學反應工程SOLUTIONTheconcentrationofcomponentsinthemixedfeedstreamisThesenumbersshowthatBisthelimitingcomponent,sofor75%conversionofBand,thecompositioninthereactorandintheexitstreamis化學反應工程WritingtherateandsolvingtheproblemintermsofBwehaveattheconditionswithinthereactorFornodensitychange,theperformanceequationofEq.13gives化學反應工程Hencethevolumetricflowrateintoandoutofthereactorisor

化學反應工程5.3STEADY-STATEPLUGFLOWREACTORInaplugflowreactorthecompositionofthefluidvariesfrompointtopointalongaflowpath;consequently,thematerialbalanceforareactioncomponentmustbemadeforadifferentialelementofvolumedV.ThusforreactantA,Eq.4.1becomesInput=output+disappearancebyreaction+accumulation

(10)

ReferringtoFig.5.5,weseeforvolumethat

=0化學反應工程Figure5.5

Notationforaplugflowreactor.

化學反應工程IntroducingthesethreetermsinEq.10,weobtain

Notingthat

Weobtainonreplacement(16)

=

化學反應工程This,then,istheequationwhichaccountsforAinthedifferentialsectionofreactorofvolumedV.Forthereactorasawholetheexpressionmustbeintegrated.NowFA0,thefeedrate,isconstant,butrAiscertainlydependentontheconcentrationorconversionofmaterials.Groupingthetermsaccordingly,weobtainThusorany(17)

化學反應工程Equation17allowsthedeterminationofreactorsizeforagivenfeedrateandrequiredconversion.CompareEqs.11and17.ThedifferenceisthatinplugflowrAvaries,whereasinmixedflowrA

isconstant.

Asamoregeneralexpressionforplugflowreactor,ifthefeedonwhichconversionisbased,subscript0,entersthereactorpartiallyconverted,subscripti,andleavesataconversiondesignatedbysubscriptf,wehave

or(18)

whereXA,i0化學反應工程Forthespecialcaseofconstant-densitysystems

inwhichcasetheperformanceequationcanbeexpressedintermsofconcentrations,oror(19)

化學反應工程Theseperformanceequations,Eqs.17to19,canbewritteneitherintermsofconcentrationsorconversions.Forsystemsofchangingdensityitismoreconvenienttouseconversions;however,thereisnoparticularpreferenceforconstantdensitysystems.Whateveritsform,theperformanceequationsinterre’latethe

rateofreaction,theextentofreaction,thereactorvolume,andthe

feedrate,andifanyoneofthesequantitiesisunknownitcanbefoundfromtheotherthree.

Figure5.6displaytheseperformanceequationsandshowsthatthespace-timeneededforanyparticulardutycanalwaysbefoundbynu’mericalorgraphicalintegration.化學反應工程Figure5.6Graphicalrepresentationoftheperformanceequationsforplugreactors.

化學反應工程However,forcertainsimplekineticformsanalyticintegrationispossible-andconvenient.Todothis,insertthekineticexpressionforrA

inEq.17andintegrate.Someofthesimplerintegratedformsplugareasfollows;Zero-orderhomogeneousreaction,anyconstant

(20)

First-orderirreversiblereaction,anyconstant,(21)

化學反應工程(22)

Second-orderirreversiblereaction,A+Bwithequimolarfeedor2A,anyconstant,(23)

Wherethedensityisconstant,put=0toobtainthesimplifiedperformanceequation.First-orderreversiblereaction,,,kineticapproximatedorfittedbywith

anobservedequilibriumconversion

,anyconstant

,化學反應工程(1)

Forsystemsofconstantdensity(constant-volumebatchandconstant-densityplugflow)theperformanceequationsareidentical,forplugflowise’quivalenttotforthebatchreactor,andtheequationscanbeused

interchangeably.(2)

Forsystemsofchangingdensity

thereisnodirectcorrespondencebetweenthebatchandtheplugflowequationsandthecorrectequationmustbeusedforeachparticularsituation.Inthiscasetheperformanceequationscannotbeusedinterchangeably.BycomparingthebatchexpressionsofChapter3withtheseplugflowexpressionswefind:化學反應工程EXAMPLE5.4PLUGFLOWREACTORPERFORMANCEAhomogeneousgasreactionA3Rhasareportedrateat215℃Findthespace-timeneededfor80%conversionofa50%A-50%inertfeedtoaplugflowreactoroperatingat215℃and5atm(CA0=0.0625mol/liter).化學反應工程FigureE5.4a

化學反應工程SOLUTIONForthisstoichiometryandwith50%inerts,twovolumesoffeedgaswouldgivefourvolumesofcompletelyconvertedproductgas;thusinwhichcasetheplugflowperformanceequation,Eq.17,becomes(i)

化學反應工程Theintegralcanbeevaluatedinanyoneofthreeways:graphically(做圖地),nu’merically(數值地),orana’lytically(解析地).Letusillustratethesemethods.

TableE5.4

0110.21.22280.6420.893化學反應工程Graphicalintegration.Firstevaluatethefunctiontobeintegratedatselectedvalues(seeTableE5.4)andplotthisfunction(seeFig.E5.4b).

Fig.E5.4b化學反應工程Countingsquaresorestimatingbyeyewefind

AreaNu’mericalIntegration.UsingSimpson’srule,applicabletoanevennumber(偶數)ofuniformlyspacedintervals(間隔)ontheXA

axis,wefindforthedataofTableE5.4,

(averageheight)(totalwidth)=

=

化學反應工程Ana’lyticalintegration.Fromatableofintegrals=

=

Themethodofintegrationrecommendeddependsonthesituation.Inthisproblemprobablythenu’mericalmethodisthequickestandsimplestandgivesagoodenoughanswerformostpurposes.化學反應工程Sowiththeintegralevaluated,Eq.(i)becomes化學反應工程EXAMPLE5.5PLUGFLOWREACTORVOLUME

Thehomogeneousgasdecompositionofphosphineproceedat649℃withthefirst-orderrateWhatsizeofplugflowreactoroperatingat649℃and460kPacanproduce80%conversionofafeedconsistingof40molofpurephosphineperhour?

化學反應工程FigureE5.5

化學反應工程SOLUTION

LetA=PH3,R=P4,S=H2.Thenthereactionbecomes4AR+6SwithThevolumeofplugflowreactorisgivenbyEq.20

EvaluatingtheindividualtermsinthisexpressiongivesFA0=40mol/hr

化學反應工程=hencethevolumeofreactor

k=10/hr化學反應工程EXAMPLE5.6TESTOFAKINETICEQUATIONINAPLUGFLOWREACTOR

WesuspectthatthegasreactionbetweenA,B,andRisanelementaryreversiblereactionA+BRandweplantotestthiswithexperimentsinanisothermalplugflowreactor.

DeveloptheisothermalperformanceequationforthesekineticsforafeedofA,B,andinerts.(b)Showhowtotestthisequationforanequimolar

feedofAandB.

化學反應工程SOLUTIONFeedpfA,B,andinerts.ForthiselementaryreactiontherateisAtconstantpressure,basingexpansionandconversiononsubstanceA,

LetM=CB0/CA0,M′=CR0/CA0,weobtain化學反應工程Hence,thedesignequationforplugflow,Eq.17,becomes

Inthisexpressionaccountsforthestoichiometryandforinertspresentinthefeed.(b)EquimolarfeedofAandB.ForCA0=CB0,CR0=0,andnoinerts,wehaveM=1,M′=0,εA=－0.5;hencetheexpressionforpartareducesto化學反應工程(i)

HavingV,,andXAdatafromaseriesofexperiments,separatelyevaluatetheleftsideandtherightsideofEq.(i).Fortherightside,atvariousXAevaluatef(XA),thenintegrategraphicallytogiveandthenmaketheplotofFig.E5.6.Ifthedatafallonareasonablystraightline,thenthesuggestedkineticschemecanbesaidtobesatisfactoryinthatitfitsthedata.化學反應工程FigureE5.6化學反應工程HoldingTimeandSpaceTimeforFlowReactors

Weshouldbeclearlyawareofthedistinctionbetweenthesetwomeasuresoftime,.Theyaredefinedasfollows:(6)or(8)

(24)

化學反應工程Forconstantdensitysystems(all